Subgroups — C₅×#33764 #11956484

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3061	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3058	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2232	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2220	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2218	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2215	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2186	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2113	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₅×#537	—	2	1	no	—
20	C₅×#535	—	2	1	no	—
21	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₅×#469	—	2	1	no	—
28	C₅×#469	—	2	1	no	—
29	C₅×#468	—	2	1	no	—
30	C₅×#468	—	2	1	no	—
31	C₅×#467	C₂²	1	1	yes	characteristic
32	C₅×#467	C₂²	1	1	yes	characteristic, complemented
33	C₅×#466	C₂²	1	1	yes	characteristic
34	C₅×#466	C₂²	1	1	yes	characteristic
35	C₅×#466	C₂²	1	1	yes	characteristic
36	C₅×#466	C₂²	1	1	yes	characteristic
37	C₅×#466	C₂²	1	1	yes	characteristic
38	C₅×#466	C₂²	1	1	yes	characteristic, complemented
39	C₅×#427	C₂²	1	1	yes	characteristic
40	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
41	C₅×#418	—	2	1	no	—
42	C₅×#417	—	2	1	no	—
43	C₅×#367	C₂²	1	1	yes	characteristic, complemented
44	C₅×#367	C₂²	1	1	yes	characteristic, complemented
45	C₅×#366	C₂²	1	1	yes	characteristic, complemented
46	C₅×#366	C₂²	1	1	yes	characteristic, complemented
47	C₅×#358	C₂²	1	1	yes	characteristic, complemented
48	C₅×#358	C₂²	1	1	yes	characteristic, complemented
49	C₅×#357	C₂²	1	1	yes	characteristic
50	C₅×#357	C₂²	1	1	yes	characteristic
51	C₅×#357	C₂²	1	1	yes	characteristic
52	C₅×#357	C₂²	1	1	yes	characteristic
53	C₅×#357	C₂²	1	1	yes	characteristic, complemented
54	C₅×#357	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
59	#33764	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂×C₅×#41	—	2	1	no	—
61	C₂×C₅×#41	D₄	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	2	1	no	—
63	C₅×#135	—	4	1	no	—
64	C₅×#135	—	4	1	no	—
65	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₅×SD₁₆	—	2	1	no	—
67	C₂×C₅×D₈	—	2	1	no	—
68	C₂×C₅×D₈	—	4	1	no	—
69	C₂×C₅×D₈	—	4	1	no	—
70	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
71	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
73	C₅×#131	—	4	1	no	—
74	C₅×#131	—	4	1	no	—
75	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
76	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
77	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₅×#127	—	4	1	no	—
82	C₅×#124	—	4	1	no	—
83	C₅×C₂²⋊Q₈	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	4	1	no	—
86	C₅×#121	—	2	1	no	—
87	C₅×#121	—	2	1	no	—
88	C₅×#121	—	2	1	no	—
89	C₅×#121	—	2	1	no	—
90	C₅×#121	—	2	1	no	—
91	C₅×#121	—	2	1	no	—
92	C₅×#121	—	4	1	no	—
93	C₅×#121	—	4	1	no	—
94	C₅×#121	—	4	1	no	—
95	C₅×#120	—	4	1	no	—
96	C₅×#120	—	4	1	no	—
97	C₅×#117	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₅×SD₃₂	—	4	1	no	—
100	C₅×SD₃₂	—	4	1	no	—
101	C₅×D₁₆	—	4	1	no	—
102	C₅×D₁₆	—	4	1	no	—
103	C₅×M₃₂	—	4	1	no	—
104	C₂×C₅×C₁₆	—	4	1	no	—
105	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
109	C₅×#107	—	2	1	no	—
110	C₅×#107	C₂³	1	1	yes	characteristic
111	C₅×#107	C₂³	1	1	yes	characteristic
112	C₅×#107	C₂³	1	1	yes	characteristic
113	C₅×#107	C₂³	1	1	yes	characteristic
114	C₅×#106	—	2	1	no	—
115	C₅×#103	—	2	1	no	—
116	C₅×#103	—	2	1	no	—
117	C₅×#102	—	2	1	no	—
118	C₅×#102	—	2	1	no	—
119	C₅×#102	—	2	1	no	—
120	C₅×#102	—	2	1	no	—
121	C₅×#102	—	2	1	no	—
122	C₅×#102	—	2	1	no	—
123	#3061	C₂×C₅	1	1	yes	characteristic, complemented
124	#3058	C₂×C₅	1	1	yes	characteristic, complemented
125	#2237	C₂×C₅	1	1	yes	characteristic, complemented
126	#2234	C₂×C₅	1	1	yes	characteristic, complemented
127	#2233	C₂×C₅	1	1	yes	characteristic, complemented
128	#2232	C₂×C₅	1	1	yes	characteristic, complemented
129	#2220	C₂×C₅	1	1	yes	characteristic, complemented
130	#2218	C₂×C₅	1	1	yes	characteristic, complemented
131	#2217	C₂×C₅	1	1	yes	characteristic, complemented
132	#2215	C₂×C₅	1	1	yes	characteristic, complemented
133	#2187	C₂×C₅	1	1	yes	characteristic, complemented
134	#2186	C₂×C₅	1	1	yes	characteristic, complemented
135	#2186	C₂×C₅	1	1	yes	characteristic, complemented
136	#2184	C₂×C₅	1	1	yes	characteristic, complemented
137	#2113	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	—	4	1	no	—
139	C₅×#41	—	4	1	no	—
140	C₅×#41	—	4	1	no	—
141	C₅×#41	—	4	2	no	—
142	C₅×#41	—	4	2	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	4	2	no	—
149	C₂×C₅×D₄	—	4	2	no	—
150	C₂×C₅×D₄	—	4	1	no	—
151	C₂×C₅×D₄	—	4	1	no	—
152	C₂×C₅×D₄	—	4	1	no	—
153	C₂×C₅×D₄	—	4	1	no	—
154	C₂×C₅×D₄	—	4	1	no	—
155	C₂×C₅×D₄	—	4	1	no	—
156	C₂×C₅×D₄	—	4	1	no	—
157	C₂×C₅×D₄	—	4	1	no	—
158	C₂×C₅×D₄	D₈	1	1	yes	characteristic
159	C₂×C₅×D₄	D₈	1	1	yes	characteristic
160	C₂×C₅×D₄	D₈	1	1	yes	characteristic
161	C₂²×C₄×C₅	—	4	1	no	—
162	C₂²×C₄×C₅	—	4	1	no	—
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₅×Q₁₆	—	2	1	no	—
167	C₅×Q₁₆	—	2	1	no	—
168	C₅×SD₁₆	—	4	2	no	—
169	C₅×D₈	—	2	1	no	—
170	C₅×D₈	—	2	1	no	—
171	C₅×D₈	—	2	1	no	—
172	C₅×D₈	—	2	1	no	—
173	C₅×D₈	—	2	1	no	—
174	C₅×D₈	—	2	1	no	—
175	C₅×D₈	—	4	2	no	—
176	C₅×M₁₆	—	4	1	no	—
177	C₅×M₁₆	—	4	1	no	—
178	C₅×M₁₆	—	4	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	4	1	no	—
194	C₅×C₄⋊C₄	—	4	1	no	—
195	C₅×C₄⋊C₄	—	4	1	no	—
196	C₅×C₂²⋊C₄	—	4	1	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₅×C₂²⋊C₄	—	4	1	no	—
199	C₅×C₂²⋊C₄	—	4	1	no	—
200	C₅×C₂²⋊C₄	—	4	1	no	—
201	C₅×C₂²⋊C₄	—	4	1	no	—
202	C₅×C₂²⋊C₄	—	4	1	no	—
203	C₅×C₂²⋊C₄	—	4	1	no	—
204	C₅×C₂²⋊C₄	—	4	1	no	—
205	C₄²×C₅	—	4	1	no	—
206	C₅×C₁₆	—	2	1	no	—
207	C₅×C₁₆	—	2	1	no	—
208	C₅×C₁₆	—	2	1	no	—
209	C₅×C₁₆	—	2	1	no	—
210	C₂×#135	C₂²×C₅	1	1	yes	characteristic, complemented
211	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
212	C₂×#131	C₂²×C₅	1	1	yes	characteristic
213	#537	—	2	1	no	—
214	#535	—	2	1	no	—
215	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
216	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
217	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
218	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
220	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
221	#469	—	2	1	no	—
222	#469	—	2	1	no	—
223	#468	—	2	1	no	—
224	#468	—	2	1	no	—
225	#467	C₂²×C₅	1	1	yes	characteristic
226	#467	C₂²×C₅	1	1	yes	characteristic, complemented
227	#466	C₂²×C₅	1	1	yes	characteristic
228	#466	C₂²×C₅	1	1	yes	characteristic
229	#466	C₂²×C₅	1	1	yes	characteristic
230	#466	C₂²×C₅	1	1	yes	characteristic
231	#466	C₂²×C₅	1	1	yes	characteristic
232	#466	C₂²×C₅	1	1	yes	characteristic, complemented
233	#427	C₂²×C₅	1	1	yes	characteristic
234	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
235	#418	—	2	1	no	—
236	#417	—	2	1	no	—
237	#367	C₂²×C₅	1	1	yes	characteristic, complemented
238	#367	C₂²×C₅	1	1	yes	characteristic, complemented
239	#366	C₂²×C₅	1	1	yes	characteristic, complemented
240	#366	C₂²×C₅	1	1	yes	characteristic, complemented
241	#358	C₂²×C₅	1	1	yes	characteristic, complemented
242	#358	C₂²×C₅	1	1	yes	characteristic, complemented
243	#357	C₂²×C₅	1	1	yes	characteristic
244	#357	C₂²×C₅	1	1	yes	characteristic
245	#357	C₂²×C₅	1	1	yes	characteristic
246	#357	C₂²×C₅	1	1	yes	characteristic
247	#357	C₂²×C₅	1	1	yes	characteristic, complemented
248	#357	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
250	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
251	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂³×C₅	—	4	1	no	—
254	C₂³×C₅	—	4	1	no	—
255	C₂³×C₅	—	4	1	no	—
256	C₂³×C₅	—	8	2	no	—
257	C₂³×C₅	—	16	1	no	—
258	C₂³×C₅	—	16	1	no	—
259	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
260	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
261	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
262	C₅×Q₈	—	4	1	no	—
263	C₅×Q₈	—	4	1	no	—
264	C₅×Q₈	—	4	1	no	—
265	C₅×D₄	—	4	1	no	—
266	C₅×D₄	—	4	1	no	—
267	C₅×D₄	—	4	1	no	—
268	C₅×D₄	—	4	1	no	—
269	C₅×D₄	—	4	1	no	—
270	C₅×D₄	—	4	1	no	—
271	C₅×D₄	—	4	1	no	—
272	C₅×D₄	—	4	1	no	—
273	C₅×D₄	—	4	1	no	—
274	C₅×D₄	—	8	2	no	—
275	C₅×D₄	—	8	2	no	—
276	C₅×D₄	—	16	1	no	—
277	C₅×D₄	—	16	1	no	—
278	C₅×D₄	—	16	1	no	—
279	C₅×D₄	—	16	1	no	—
280	C₅×D₄	—	16	1	no	—
281	C₅×D₄	—	16	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	8	2	no	—
294	C₂×C₄×C₅	—	16	1	no	—
295	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
299	C₅×C₈	—	2	1	no	—
300	C₅×C₈	—	2	1	no	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
303	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×#41	—	2	1	no	—
305	C₂×#41	C₅×D₄	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	#135	—	4	1	no	—
308	#135	—	4	1	no	—
309	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×D₈	—	2	1	no	—
312	C₂×D₈	—	4	1	no	—
313	C₂×D₈	—	4	1	no	—
314	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
315	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
316	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
317	#131	—	4	1	no	—
318	#131	—	4	1	no	—
319	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
320	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
321	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
325	#127	—	4	1	no	—
326	#124	—	4	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	4	1	no	—
330	#121	—	2	1	no	—
331	#121	—	2	1	no	—
332	#121	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	4	1	no	—
337	#121	—	4	1	no	—
338	#121	—	4	1	no	—
339	#120	—	4	1	no	—
340	#120	—	4	1	no	—
341	#117	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	SD₃₂	—	4	1	no	—
344	SD₃₂	—	4	1	no	—
345	D₁₆	—	4	1	no	—
346	D₁₆	—	4	1	no	—
347	M₃₂	—	4	1	no	—
348	C₂×C₁₆	—	4	1	no	—
349	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
352	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
353	#107	—	2	1	no	—
354	#107	C₂³×C₅	1	1	yes	characteristic
355	#107	C₂³×C₅	1	1	yes	characteristic
356	#107	C₂³×C₅	1	1	yes	characteristic
357	#107	C₂³×C₅	1	1	yes	characteristic
358	#106	—	2	1	no	—
359	#103	—	2	1	no	—
360	#103	—	2	1	no	—
361	#102	—	2	1	no	—
362	#102	—	2	1	no	—
363	#102	—	2	1	no	—
364	#102	—	2	1	no	—
365	#102	—	2	1	no	—
366	#102	—	2	1	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	1	no	—
370	C₂²×C₅	—	2	1	no	—
371	C₂²×C₅	—	2	1	no	—
372	C₂²×C₅	—	2	1	no	—
373	C₂²×C₅	—	2	1	no	—
374	C₂²×C₅	—	2	1	no	—
375	C₂²×C₅	—	2	1	no	—
376	C₂²×C₅	—	8	1	no	—
377	C₂²×C₅	—	8	1	no	—
378	C₂²×C₅	—	8	1	no	—
379	C₂²×C₅	—	8	1	no	—
380	C₂²×C₅	—	8	1	no	—
381	C₂²×C₅	—	8	1	no	—
382	C₂²×C₅	—	8	1	no	—
383	C₂²×C₅	—	8	1	no	—
384	C₂²×C₅	—	8	1	no	—
385	C₂²×C₅	—	16	4	no	—
386	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	2	1	no	—
389	C₄×C₅	—	2	1	no	—
390	C₄×C₅	—	8	1	no	—
391	C₄×C₅	—	8	1	no	—
392	C₄×C₅	—	8	1	no	—
393	C₄×C₅	—	8	1	no	—
394	C₄×C₅	—	8	1	no	—
395	C₄×C₅	#534	1	1	yes	characteristic
396	C₄×C₅	#575	1	1	yes	characteristic
397	C₂⁴	—	4	1	no	—
398	#41	—	4	1	no	—
399	#41	—	4	1	no	—
400	#41	—	4	2	no	—
401	#41	—	4	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	C₅×D₈	1	1	yes	characteristic
418	C₂×D₄	C₅×D₈	1	1	yes	characteristic
419	C₂×D₄	C₅×D₈	1	1	yes	characteristic
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	Q₁₆	—	2	1	no	—
426	Q₁₆	—	2	1	no	—
427	SD₁₆	—	4	2	no	—
428	D₈	—	2	1	no	—
429	D₈	—	2	1	no	—
430	D₈	—	2	1	no	—
431	D₈	—	2	1	no	—
432	D₈	—	2	1	no	—
433	D₈	—	2	1	no	—
434	D₈	—	4	2	no	—
435	M₁₆	—	4	1	no	—
436	M₁₆	—	4	1	no	—
437	M₁₆	—	4	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	4	1	no	—
459	C₂²⋊C₄	—	4	1	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₄²	—	4	1	no	—
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₁₆	—	2	1	no	—
468	C₁₆	—	2	1	no	—
469	C₂×C₅	—	4	1	no	—
470	C₂×C₅	—	4	1	no	—
471	C₂×C₅	—	4	1	no	—
472	C₂×C₅	—	16	1	no	—
473	C₂×C₅	—	16	1	no	—
474	C₂×C₅	—	16	1	no	—
475	C₂×C₅	#3186	1	1	yes	characteristic
476	C₂×C₅	#3415	1	1	yes	characteristic
477	C₂×C₅	#3416	1	1	yes	characteristic
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	8	2	no	—
482	C₂³	—	16	1	no	—
483	C₂³	—	16	1	no	—
484	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
485	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
486	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
487	Q₈	—	4	1	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	8	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	16	1	no	—
502	D₄	—	16	1	no	—
503	D₄	—	16	1	no	—
504	D₄	—	16	1	no	—
505	D₄	—	16	1	no	—
506	D₄	—	16	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	16	1	no	—
520	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
521	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
522	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
528	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
529	C₅	#33764	1	1	yes	characteristic, direct product factor, Sylow
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	16	4	no	—
549	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₅×#534	1	1	yes	characteristic
559	C₄	C₅×#575	1	1	yes	characteristic
560	C₂	—	4	1	no	—
561	C₂	—	4	1	no	—
562	C₂	—	4	1	no	—
563	C₂	—	16	1	no	—
564	C₂	—	16	1	no	—
565	C₂	—	16	1	no	—
566	C₂	C₅×#3186	1	1	yes	characteristic
567	C₂	C₅×#3415	1	1	yes	characteristic
568	C₂	C₅×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×#131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#3061	C₂	semidirect
2. C₅×#3058	C₂	semidirect
3. C₅×#2237	C₂	semidirect
4. C₅×#2234	C₂	semidirect
5. C₅×#2233	C₂	semidirect
6. C₅×#2232	C₂	semidirect
7. C₅×#2220	C₂	semidirect
8. C₅×#2218	C₂	semidirect
9. C₅×#2217	C₂	semidirect
10. C₅×#2215	C₂	semidirect
11. C₅×#2187	C₂	semidirect
12. C₅×#2186	C₂	semidirect
13. C₅×#2186	C₂	semidirect
14. C₅×#2184	C₂	semidirect
15. C₅×#2113	C₂	semidirect
16. C₂×C₅×#135	C₂²	semidirect
25. C₂×C₅×M₃₂	C₂²	semidirect
26. C₂²×C₅×C₁₆	C₂²	semidirect
32. C₅×#467	C₂²	semidirect
38. C₅×#466	C₂²	semidirect
40. C₂×C₅×#107	C₂²	semidirect
43. C₅×#367	C₂²	semidirect
44. C₅×#367	C₂²	semidirect
45. C₅×#366	C₂²	semidirect
46. C₅×#366	C₂²	semidirect
47. C₅×#358	C₂²	semidirect
48. C₅×#358	C₂²	semidirect
53. C₅×#357	C₂²	semidirect
54. C₅×#357	C₂²	semidirect
57. C₅×C₂²⋊C₁₆	C₂²	semidirect
58. C₅×C₂²⋊C₁₆	C₂²	semidirect
59. #33764	C₅	direct (N × H)
123. #3061	C₂×C₅	semidirect
124. #3058	C₂×C₅	semidirect
125. #2237	C₂×C₅	semidirect
126. #2234	C₂×C₅	semidirect
127. #2233	C₂×C₅	semidirect
128. #2232	C₂×C₅	semidirect
129. #2220	C₂×C₅	semidirect
130. #2218	C₂×C₅	semidirect
131. #2217	C₂×C₅	semidirect
132. #2215	C₂×C₅	semidirect
133. #2187	C₂×C₅	semidirect
134. #2186	C₂×C₅	semidirect
135. #2186	C₂×C₅	semidirect
136. #2184	C₂×C₅	semidirect
137. #2113	C₂×C₅	semidirect
210. C₂×#135	C₂²×C₅	semidirect
219. C₂×M₃₂	C₂²×C₅	semidirect
220. C₂²×C₁₆	C₂²×C₅	semidirect
226. #467	C₂²×C₅	semidirect
232. #466	C₂²×C₅	semidirect
234. C₂×#107	C₂²×C₅	semidirect
237. #367	C₂²×C₅	semidirect
238. #367	C₂²×C₅	semidirect
239. #366	C₂²×C₅	semidirect
240. #366	C₂²×C₅	semidirect
241. #358	C₂²×C₅	semidirect
242. #358	C₂²×C₅	semidirect
247. #357	C₂²×C₅	semidirect
248. #357	C₂²×C₅	semidirect
251. C₂²⋊C₁₆	C₂²×C₅	semidirect
252. C₂²⋊C₁₆	C₂²×C₅	semidirect
529. C₅	#33764	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3061	2
C₅×#3058	2
C₅×#2237	2
C₅×#2234	2
C₅×#2233	2
C₅×#2232	2
C₅×#2220	2
C₅×#2218	2
C₅×#2217	2
C₅×#2215	2
C₅×#2187	2
C₅×#2186	2
C₅×#2184	2
C₅×#2113	2
#33764	5

Subgroups — C5×#33764 #11956484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33764 #11956484